Yours is an odd bit of reasoning.
What is the prohibitive correlation between democracy, a form of government, and the death penalty, a form of punishment?
Although, I'd have to agree no one has yet figured out how to take it with them beyond the beyond, you'll have to sketch in a mighty elastic enthymeme to leap from "No state, no society should be allowed to kill its citizens" to "[the] death penalty isn't compatible with a democracy".
Let's examine this governing principle of your main proposition: "No state, no society should be allowed to kill its citizens".
1. A policeman is an agent of a local government, an officer of its courts. Your principle then would prohibit said policeman, with opportunity, from using deadly force to kill a citizen husband holding at gunpoint his citizen wife with the unmistakable intent of killing her.
2. An air national guardsman is an agent of the state government. Charged with the protection of the local citizenry, your principle would prohibit said guardsman from shooting down a plane flown by a citizen crazy with the unmistakable intent of crashing into an occupied building and killing as many of his fellow citizens as possible.
3. A member of the armed forces is an agent of the national government. Your principle again would limit the exercise of protecting the duly elected government against renegade citizens leading a coup d'état to, what? Tongue-clucking?
Your principle is quite the boon to the lawless.
As I've written elsewhere, rights, in law, are neither inherent nor irrevocable. They are a class of entitlements, they proceed from the government. When one speaks of "inalienable" rights, one must look beyond government to a supernatural authority. You ask that a government stand guaranty for that which is beyond its claims. Well, that's a neat trick.
Further I would venture that rights are relational. If you were the sole being in the world, what rights would you enjoy? Life? Liberty? Estate? These rights all require society for context, which is to say, meaning. Their establishment and protection require a competent grantor, which is to say, an authority. M./Mll. Lestat, I doubt you are here to make the case for God. However I fully understand your trepidation at the thought of your rights in the safekeeping of the Fifth Republic. Bonne chance.